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Mathematics of Finance III (ACTL90003)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

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Semester 1
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This subject aims to provide students with grounding in advanced financial mathematics, covering option pricing under the binomial model; risk‐neutral pricing of derivative securities; Brownian motion; introduction to Itô΄ formula and SDEs; stochas􀆟 asset models; Black‐Scholes model; arbitrage and hedging; interest‐rate models; actuarial applications and simple models for credit risk.

Intended learning outcomes

On successful completion of this subject a student should be able to:



  • Demonstrate a knowledge of the properties of option prices, valuation methods and hedging techniques, and be able to apply these;
  • Show how to use binomial trees and lattices in valuing options;
  • Apply the Ito calculus;
  • Derive option prices under the Black-Scholes model;
  • Describe and apply in simple models, including the binomial model and the Black-Scholes model, the approach to pricing using deflators and demonstrate its equivalence to the risk-neutral pricing approach;
  • Demonstrate a knowledge of models of the term structure of interest rates;
  • Describe, as a computational tool, the risk-neutral approach to the pricing of zero coupon bonds and interest-rate derivatives for a general one-factor diffusion model for the risk-free rate of interest;
  • Demonstrate a knowledge of simple models for credit risk.

Generic skills

High level of development:

  • Written communication;
  • Problem solving;
  • Mathematical reasoning;
  • Simple models of credit risk;
  • Application of theory to practice;
  • Interpretation and analysis.

Last updated: 8 November 2024